Where does logic end and trial-and-error start? To me, that line seems blurred. It’s clear that techniques such as pairs, triples, etc., wings, fish, coloring, strong links, rectangles, and the like fall into the category of logic, but it’s the chains that have me wondering.

Suppose one decides to start a forcing chain based in a two-candidate cell. Or he sees that a number can occur only twice in a certain box and decides to test for each of the possible occurrences. It seems that the actions taken from these chains are based on logic; for example, cell such-and-such is “X” for either value, therefore, that cell must be “X.” But the deciding where to start these tests seems to have an element of trial-and-error to it, unless, of course, there is some sort of logic that tells one where to start the chain.

So where do YOU draw the line? How do you define trial-and-error? What does a puzzle constructor have in mind when he guarantees that his puzzles are all solvable by logic, without resorting to trial-and-error?

But the deciding where to start these tests seems to have an element of trial-and-error to it...

I used to feel that way about chains until I thought about in a different manner. Is it guessing if you look at two cells for a hidden pair and you don't find one? If you do find one is it guessing if you had to look in three cells before you found it? Is it guessing if you make a colouring chain that doesn't lead to an exclusion? Is it guessing if you see two bi-value cells and look for but can't find the third one to make an 'xy-wing'? Nobody questions the logic of these techniques once found but nobody asks if there was a logical reason to look for it where it was found either.

If we don't hold other techniques to an arbitrary "what logic told you to look in that cell" criteria, why should it be done for forcing chains? If we accept the logic of a forcing chain, it shouldn't really matter how it was found, any more than it does for any other technique that is used.

To me, "trial and error" means outright guessing -- just enter a value in some cell, and try to work the puzzle. If it works out, you're done -- if not, go back to the starting point and make another guess.

I think that Alan R is the only regular poster on this forum who wants to define forcing chains as "T&E". dcb

An backtracking analog is to solve a maze: Unroll a ball of string to mark your path. Go anywhere. If you reach a dead end, back up to the last intersection (with your string), mark the passage as no good, and try any other unmarked path. Guaranteed to work, but most would agree this is trial and error.

But I do frequently see references to trial-and-error and am just trying to find out what people mean by it.

I don't think there is a blanket answer for that. IMO some people use the term 'trial & error' in reference to a technique or pattern that they either don't understand or one in which they don't see/accept the logic. (Which for quite a while for me was a forcing chain, until I thought about it in the terms above.) Others use the term for techniques similar to those described by David and Keith, and that seems to be the concensus on those techniques.